arXiv subjects

Michael Lang

Publications and source records attributed to Michael Lang.

At least 37 records · Page 2Linked to original sources

arXiv2021

Involvement of structural dynamics in the charge-glass formation in molecular metals

We present a combined study of thermal expansion and resistance fluctuation spectroscopy measurements exploring the static and dynamic aspects of the charge-glass formation in the quasi-two-dimensional organic conductors $θ$-(BEDT-TTF)$_2$$MM^\prime$(SCN)$_4$ with $M$ = Cs and $M^\prime$ = Co,Zn. In these materials, the emergence of a novel charge-glass state so far has been interpreted in purely electronic terms by considering the strong frustration of the Coulomb interactions on a triangular lattice. Contrary to this view, we provide comprehensive evidence for the involvement of a \textit{structural} glass-like transition at $T_{\text{g}} \sim 90-100\,$K. This glassy transition can be assigned to the freezing of structural conformations of the ethylene endgroups in the donor molecule with an activation energy of $E_{\rm{a}}\approx 0.32\,$eV, and the concomitant slowing down of the charge carrier dynamics is well described by a model of non-exponential kinetics. These findings discolse an important aspect of the phase diagram and renders the current understanding of the charge-glass state in the whole family of $θ$-(BEDT-TTF)$_2MM^\prime$(SCN)$_4$ incomplete. Our results suggest that the entanglement of slow structural and charge-cluster dynamics due to the intimate coupling of lattice and electronic degrees of freedom determine the charge-glass formation under geometric frustration.

cond-mat.str-el↗

arXiv2021

Spin Vortex Crystal Order in Organic Triangular Lattice Compound

Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates, such as $κ$-(ET)$_2$Cu$_2$(CN)$_3$ ($κ$-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring-exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this work, we discuss the properties of the recently synthesized $κ$-(BETS)$_2$Mn[N(CN)$_2$]$_3$ ($κ$-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring-exchange in these materials, and support the proposed chiral spin-liquid scenario for triangular lattice organics.

cond-mat.str-el↗

arXiv2021

Competing exchange and irreversible reactions in a linear co-polycondensation lead to a broad composition window where tunable high molecular weight polymers can be prepared

A co-polycondensation reaction is discussed analytically and by Monte-Carlo simulations where two reactive units compete for reactions with an alternating third reactive unit, whereby irreversible reactions replace bonds which are able to undergo exchange reactions. The resulting number average molar mass, $M_{\text{n}}$, exhibits only one distinct peak at the stoichiometric condition of both competitors with the alternating partner. The weight average molar mass, $M_{\text{w}}$, reaches an additional second peak at the stoichiometric condition between the dominating competitor and the alternating partner. Both peaks of $M_{\text{w}}$ surround a range of compositions where a rather high and approximately constant $M_{\text{w}}$ is obtained. The degree of polymerization of the dominating and alternating reaction partners is rather insensitive towards composition fluctuations if the reaction mixture remains within this composition window. This promotes high molecular weight species and more homogeneous weight distributions at incomplete mixing conditions. An ideal reference case (identical reaction rates for all reactions) is solved analytically to describe these reactions. The position of the stable composition window and the average molar masses inside this window can be tuned by choosing appropriate precursor molecules, reaction mixtures or post-tuning steps at later times.

cond-mat.soft↗

arXiv2021

Excluded volume effects in polymer brushes at moderate chain stretching

We develop a strong stretching approximation for a polymer brush made of self-avoiding polymer chains. The density profile of the brush and the distribution of the end monomer positions in stretching direction are computed and compared with simulation data. We find that our approach leads to a clearly better approximation as compared to previous approaches based upon Gaussian elasticity at low grafting densities (moderate chain stretching), for which corrections due to finite extensibility can be ignored.

cond-mat.soft↗

arXiv2021

The Formation and Structure of Olympic Gels

Different methods for creating Olympic gels are analyzed using computer simulations. First ideal reference samples are obtained from freely interpenetrating semi-dilute solutions and melts of cyclic polymers. The distribution of pairwise concatenations per cyclic molecule is given by a Poisson-distribution and can be used to describe the elastic structure of the gels. Several batches of linear chains decorated with different selectively binding groups at their ends are mixed in the "DNA Origami" technique and network formation is realized. While the formation of cyclic molecules follows mean field predictions below overlap of the precursor molecules, an enhanced ring formation above overlap is found that is not explained by mean field arguments. The "progressive construction" method allows to create Olympic gels with a single reaction step from a concentrated mixture of large compressed rings with a low weight fraction short chains that are below overlap concentration. This method, however, is limited by the difficulty to obtain a sufficiently high degree of polymerization of the large rings.

cond-mat.soft↗

arXiv2021

Arm retraction dynamics in dense polymer brushes

Large scale Monte Carlo simulations of dense layers of grafted polymer chains in good solvent conditions are used to explore the relaxation of a polymer brush. Monomer displacements are analyzed for the directions parallel and perpendicular to the grafting plane. Auto-correlation functions of individual segments or chain sections are monitored as function of time. We demonstrate that the terminal relaxation time $τ$ of grafted layers well in the brush regime grows exponentially with degree of polymerization $N$ of the chains, $τ\propto N^{3}\exp(N/N_{e})$, with $N_{e}$ the entanglement degree of polymerization in the brush. One specific feature of entangled polymer brushes is that the late time relaxation of the perpendicular component coincides for all segments. We use this observation to extract the terminal relaxation time of an entangled brush.

cond-mat.soft↗

arXiv2021

An Analysis of the Gel Point of Polymer Model Networks by Computer Simulations

The gel point of end-linked model networks is determined from computer simulation data. It is shown that the difference between the true gel point conversion, $p_{\text{c}}$, and the ideal mean field prediction for the gel point, $p_{\text{c,id}}$, is a function of the average number of cross-links per pervaded volume of a network strand, $P$, and thus, contains an explicit dependence on junction functionality $f$. On the contrary, the amount of intra-molecular reactions at the gel point is independent of $f$ in a first approximation and exhibits a different power law dependence on the overlap number of elastic strands as compared to the gel point delay $p_{\text{c}}-p_{\text{c,id}}$. Therefore, $p_{\text{c}}-p_{\text{c,id}}$ cannot be predicted from intra-molecular reactions and vice versa in contrast to a long standing proposal in literature. Instead, the main contribution to $p_{\text{c}}-p_{\text{c,id}}$ for $P>1$ arises from the extra bonds (XB) needed to bridge the gaps between giant molecules separated in space and scales roughly $\propto\left(P-1\right)^{-1/2}$. Further corrections to scaling are due to non-ideal reaction kinetics, composition fluctuations, and incompletely screened excluded volume, which are discussed briefly.

cond-mat.soft↗

arXiv2021

Elasticity of Phantom Model Networks with Cyclic Defects

The impact of finite cycles on the phantom modulus in an otherwise perfect network is computed exactly. It is shown that pending cycles reduce the phantom modulus of the network by $kT/V$ independent of junction functionality. The correction for nonpending cycles is larger than estimated previously within this particular approximation of the surrounding network structure. It is discussed that loop formation inevitably leads to streched chain conformations, if the loops are built step by step as part of the network structure. All network loops tend to contract simultaneously to optimize conformations, which leads to an increasing stretch of chains in larger loops that can be observed in computer simulations. Possible other corrections to the phantom modulus that were left aside in previous work are discussed briefly.

cond-mat.soft↗

arXiv2021

Effect of Topology on the Conformations of Ring Polymers

The bond fluctuation method is used to simulate both non-concatenated entangled and interpenetrating melts of ring polymers. We find that the swelling of interpenetrating rings upon dilution follows the same laws as for linear chains. Knotting and linking probabilities of ring polymers in semi-dilute solution are analyzed using the HOMFLY polynomial. We find an exponential decay of the knotting probability of rings. The correlation length of the semi-dilute solution can be used to superimpose knotting data at different concentrations. A power law dependence $f_{n}\simϕR^{2}\simϕ^{0.77}N$ for the average number $f_{n}$ of linked rings per ring at concentrations larger than the overlap volume fraction of rings $ϕ^{*}$ is determined from the simulation data. The fraction of non-concatenated rings displays an exponential decay $P_{OO}\sim\exp(-f_{n})$, which indicates $f_{n}$ to provide the entropic effort for not forming concatenated conformations. Based upon this results we find four different regimes for the conformations of rings in melts that are separated by a critical lengths $N_{OO}$, $N_{C}$ and $N^{*}$. $N_{OO}$ describes the onset of the effect of non-concatenation below which topological effects are not important, $N_{C}$ is the cross-over between weak and strong compression of rings, and $N^{*}$ is defined by the cross-over from a non-concatenation contribution $f_{n}\simϕR^{2}$ to an overlap dominated concatenation contribution $f_{n}\simϕN^{1/2}$ at $N>N^{*}$. For $N_{OO}<N<N_{C}$, the scaling of ring sizes $R\sim N^{2/5}$ results from balancing non-concatenation with weak compression of rings. For $N_{C}<N<N^{*}$, non-concatenation and strong compression imply $R\sim N^{3/8}$. Our simulation data for non-interpenetrating rings up to $N=1024$ are in good agreement with the prediction for weakly compressed rings.

cond-mat.soft↗

arXiv2021

On the Elasticity of Polymer Model Networks Containing Finite Loops

Based upon the resistor analogy and using the ideal loop gas approximation(ILGA) it is shown that only pending loops reduce the modulus of an otherwise perfect network made of monodisperse strands and junctions of identical functionality. Thus, the cycle rank of the network with pending structures removed (cyclic and branched) is sufficient to characterize modulus, if the resistor analogy can be employed. It is further shown that it is impossible to incorporate finite cycles into a polymer network such that individual network strands are at equilibrium conformations while maintaining simultaneously a force balance at the junctions. Therefore, the resistor analogy provides only an approximation for the phantom modulus of networks containing finite loops. Improved approaches to phantom modulus can be constructed from considering a force balance at the junctions, which requires knowledge of the distribution of cross-link fluctuations in imperfect networks. Assuming loops with equilibrium conformations and a force balance at all loop junctions, a lower bound estimate for the phantom modulus, $G_{\text{ph}}\approx\left(ξ-c_{\text{f}}L_{1}\right)kT/V$ is obtained within the ILGA for end-linked model networks and in the limit of $L_{1}\llξ$. Here, $L_{1}$ is the number of primary ("pending") loops, $ξ$ the cycle rank of the network, $k$ the Boltzmann constant, $V$ the volume of the sample, and $T$ the absolute temperature. $c_{\text{f}}$ is a functionality dependent coefficient that is $\approx2.56$ for junction functionality $f=3$ and $\approx3.06$ for $f=4$, while it converges quickly towards $\approx4.2$ in the limit of large $f$. Further corrections to phantom modulus beyond finite loops are addressed briefly.

cond-mat.soft↗

arXiv2021

On the Structure of Star-Polymer Networks

Using the bond fluctuation model we study polymer networks obtained by endlinking of symmetric 4-arm star polymers. We consider two types of systems. Solutions of one type (A) of star polymers and solution of two types (A,B) of star polymer where A-type polymers can only crosslink with B-type polymers. We find that network defects in $A$ networks are dominated by short dangling loops close to overlap concentration $c^{*}$. $AB$ networks develop a more perfect network structure, since loop sizes involving an odd number of stars are impossible, and thus, the most frequent dangling loop with largest impact on the phantom modulus is absent. The analysis of the pair-correlation and scattering function reveals that there is an amorphous packing of $A$ and $B$ type stars with a homogenization of $A$ and $B$ concentrations upon cross-linking at intermediate length scales in contrast to the previously suggested crystalline like order of $A$ and $B$ components at $c^{*}$. This result is corroborated by the coincidence of the probabilities of the shortest loop structures (which is impossible upon the previously suggested packing of stars) in both types of networks. Furthermore, we derive the vector order parameters associated with the most frequent network structures based on the phantom model. In particular, for $AB$ networks we can show that there is a dominating cyclic defect with a clearly separated order parameter that could be used to analyze cyclic network defects.

cond-mat.soft↗

arXiv2021

Short Cyclic Structures in Polymer Model Networks: A Test of Mean Field Approximation by Monte Carlo Simulations

A mean field rate theory description of the homo- and co-polymerization of $f$-functional molecules is developed, which contains the formation of short cyclic structures inside the network. The predictions of this model are compared with Monte-Carlo simulations of cross-linking of star polymers in solution. We find that homo-polymerizations are well captured by mean-field models at concentrations larger than one quarter of the geometrical overlap concentration. All simulation data can be fit using a single geometric parameter for cyclization. The simulation data reveal that within the range of parameters of the present study correlations among multiply connected molecules can be neglected. Thus, mean-field treatments of homopolymerizations are reasonable approximations, if short cycles are properly addressed. Co-polymerization is considered in the case of strict A-B reactions, where all reactive groups of individual molecules are either of type A or B. For these systems we find a clear influence of the local intermixing of A and B groups for all concentrations investigated. In consequence, mean-field models are less appropriate to describe the simulation data. The lack of ring structures containing an odd number of molecules as compared to homopolymerizations at the same extent of reaction allows for the formation of stable AB networks at concentrations one order of magnitude below the geometrical overlap concentration.

cond-mat.soft↗

arXiv2021

Ring conformations in bidisperse blends of ring polymers

The size of rings (also called cyclic polymers) in bidisperse blends of chemically identical rings is analyzed by computer simulations. Data of entangled ring blends and blends of interpenetrating rings are compared and it is shown that the compression of entangled rings can be explained by the changes in the penetrable fraction of the minimal surface bounded by the ring. Corrections for small rings can be approximated by a concatenation probability $1-P_{OO}$ that a ring entraps at least one other ring. Both results are in line with a previous work [1] to explain the compression of entangled rings in monodisperse melts. Bond-bond correlations in melts of interpenetrating rings lead to similar corrections for ring sizes as reported previously [2] for monodisperse linear melts. For entangled rings, bond-bond correlations show an anti-correlation peak at a curvilinear distance of about ten segments that coincides with a horizontal tangent in the normalized mean square internal distances along the ring. Both observations become independent of melt molecular weight for sufficiently large degrees of polymerization and such behavior is not found in samples with entanglements switched off. In consequence, the length scale of topological interactions (entanglement length) in a melt of entangled rings must be considered as constant in contrast to a recent proposal by Sakaue [3].

cond-mat.soft↗

arXiv2021

Monomer Fluctuations and the Distribution of Residual Bond Orientations in Polymer Networks

In the present work, four series of simulations are analyzed: entangled model networks of a) mono-disperse or b) poly-disperse weight distribution between the crosslinks, c) non-entangled phantom model networks and d) non-entangled model networks with excluded volume interactions. Previous work on the average residual bond orientations (RBO) of model networks [1] is extended to describe the distribution of RBOs for the entangled networks of the present study. The phantom model can be used to describe the monomer fluctuations, average RBOs, and the distribution of RBOs in networks without entanglements and without excluded volume. Monomer fluctuations in networks with excluded volume but without entanglements can be described if the phantom model is corrected by the effect of the incompletely screened excluded volume. It is shown that parameters of the tube model can be determined from monomer fluctuations in polymer networks and from the RBO. A scaling of the RBO $\propto N^{-1/2}$ is observed in both mono-disperse and poly-disperse entangled networks, while for all networks without entanglements an RBO $\propto N^{-1}$ is found. The distribution of the RBO of entangled samples can be described by assuming a normal distribution of tube lengths that is broadened by local fluctuations in tube curvature. Both observables, monomer fluctuations and RBO, are in agreement with slip link or slip tube models [2] for networks and disagree with network models that do not allow a sliding motion of the monomers along a confining tube.

cond-mat.soft↗

arXiv2021

The Swelling of Olympic Gels

The swelling equilibrium of Olympic gels, which are composed of entangled cyclic polymers, is studied by Monte Carlo Simulations. In contrast to chemically crosslinked polymer networks, we observe that Olympic gels made of chains with a \emph{larger} degree of polymerization, $N$, exhibit a \emph{smaller} equilibrium swelling degree, $Q\propto N^{-0.28}ϕ_{0}^{-0.72}$, at the same polymer volume fraction $ϕ_{0}$ at network preparation. This observation is explained by a desinterspersion process of overlapping non-concatenated rings upon swelling.

cond-mat.soft↗

arXiv2021

Olympic Gels: Concatenation and Swelling

Concatenation and equilibrium swelling of Olympic gels, which are composed of entangled cyclic polymers, is studied by Monte Carlo Simulations. The average number of concatenated molecules per cyclic polymers, $f_n$, is found to depend on the degree of polymerization, $N$, and polymer volume fraction at network preparation, $ϕ_0$, as $f_n ~ ϕ_0^{ν/(3ν-1)}N$ with scaling exponent $ν = 0.588$. In contrast to chemically cross-linked polymer networks, we observe that Olympic gels made of longer cyclic chains exhibit a smaller equilibrium swelling degree, $Q ~ N^{-0.28} ϕ_0^{-0.72}$, at the same polymer volume fraction $ϕ_0$. This observation is explained by a desinterspersion process of overlapping non-concatenated rings upon swelling, which is tested directly by analyzing the change in overlap of the molecules upon swelling.

cond-mat.soft↗

arXiv2020

Lattice dynamics coupled to charge and spin degrees of freedom in the molecular dimer-Mott insulator $κ$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl

Inelastic neutron scattering measurements on the molecular dimer-Mott insulator $κ$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl reveal a phonon anomaly in a wide temperature range. Starting from $T_{\rm ins}\sim50$-$60$ K where the charge gap opens, the low-lying optical phonon modes become overdamped upon cooling towards the antiferromagnetic ordering temperature $T_\mathrm{N} = 27$ K, where also a ferroelectric ordering at $T_{\rm FE} \approx T_{\rm N}$ occurs. Conversely, the phonon damping becomes small again when spins and charges are ordered below $T_\mathrm{N}$, while no change of the lattice symmetry is observed across $T_\mathrm{N}$ in neutron diffraction measurements. We assign the phonon anomalies to structural fluctuations coupled to charge and spin degrees of freedom in the BEDT-TTF molecules.

cond-mat.str-el↗

arXiv2020

Steady-state nucleosynthesis throughout the Galaxy

Measurement and astrophysical interpretation of characteristic gamma-ray lines from nucleosynthesis was one of the prominent science goals of the INTEGRAL mission and in particular its spectrometer SPI. Emission from 26Al and from 60Fe decay lines originates from accumulated ejecta of nucleosynthesis sources, and appears diffuse in nature. 26Al and 60Fe are believed to originate mostly from massive star clusters. Gamma-ray observations open an interesting window to trace the fate and flow of nucleosynthesis ejecta, after they have left the immediate sources and their birth sites, and on their path to mix with ambient interstellar gas. The INTEGRAL 26Al emission image confirms earlier findings of clumpiness and an extent along the entire plane of the Galaxy, supporting its origin from massive-star groups. INTEGRAL spectroscopy resolved the line and found Doppler broadenings and systematic shifts from large-scale galactic rotation. But an excess velocity of ~200 km/s suggests that 26Al decays preferentially within large superbubbles that extend in forward directions between spiral arms. The detection of 26Al line emission from nearby Orion and the Eridanus superbubble supports this interpretation. Positrons from beta+ decays of 26Al and other nucleosynthesis ejecta have been found to not explain the morphology of positron annihilation gamma-rays at 511 keV that have been measured by INTEGRAL. The 60Fe signal measured by INTEGRAL is diffuse but too weak for an imaging interpretation, an origin from point-like/concentrated sources is excluded. The 60Fe/26Al ratio is constrained to a range 0.2-0.4. Beyond improving precision of these results, diffuse nucleosynthesis contributions from novae (through 22Na radioactivity) and from past neutron star mergers in our Galaxy (from r-process radioactivity) are exciting new prospects for the remaining mission extensions.

astro-ph.IM↗